Comprehensive Notes on Statistical Tests and Research Methodology

Non-parametric Tests

• Non-parametric tests are used when data violates assumptions of parametric tests, such as skewed data.
• These tests can be conducted using statistical software similar to parametric tests.

Test Options

Parametric Tests

• Pearson’s r: Measures the strength and direction of the relationship between two continuous variables.
• Independent Samples t-test: Compares means between two independent groups.
• Paired Samples t-test: Compares means from the same group at different times.
• ANOVA (Analysis of Variance):
  • Independent ANOVA: Compares means among three or more independent groups.
  • Repeated ANOVA: Compares means among three or more related groups.

Non-Parametric Tests

• Spearman’s rho: Non-parametric measure of rank correlation.
• Mann–Whitney U Test: Non-parametric alternative to the independent samples t-test when the norm violations are present.
• Welch’s t-test: Used when variances are unequal.
• Wilcoxon Signed-Rank Test: Non-parametric alternative to the paired samples t-test.
• Kruskal-Wallis ANOVA: Non-parametric alternative for one-way ANOVA.
• Friedman’s ANOVA: Non-parametric alternative for repeated measures ANOVA.

Chi-Square Tests

• Chi-square Test: Used for analyzing categorical data to determine if frequency data is significantly different from what is expected.
• One-variable Chi-square tests: Test for one categorical variable.

Proportion Tests

• Examined different outcomes for proportions, which can include:
  • Religious affiliation (Yes/No)
  • Preference for white or yellow light

Example of Proportion Test Output:

• Proportions:
  • N: 39 → 0.722 (count)
  • Y: 15 → 0.278 (count)
  • White light: 26 → 0.481 (count)
  • Yellow light: 28 → 0.519 (count)
• Goodness of Fit Statistics:
  • x^2 = 10.7, df = 1, p < 0.001 (significant)
  • x^2 = 0.0741, df = 1, p = 0.785 (not significant)

Contingency Tables

• Used to analyze two categorical variables to see if there is an association between them.
• Example of a contingency table showing relationship between religion and sex.

Generalizability of Research Findings

• External Validity: Indicates the extent to which findings from a study can be generalized to other populations.
• ~70% of research conducted with college students; ~23% with external population.

Characteristics of Typical Samples

• College Students:

  • Limited age range, forming social and political attitudes.
  • High cognitive skills, may not represent broader populations.

• Volunteers:

  • Generally, more educated, higher socioeconomic status, and may yield biased results if not representative of the larger population.

• Online Research:

  • Often reflects younger demographics with issues of demographic reliability and informed consent concerns.

Ethical Practices for Internet-Based Research

• Transparency in recruitment and understanding participant privacy.
• Compliance with data protection laws and ensuring informed consent prior to participation.
• Use of unique identification codes for tracking and securing participant data.
• Prioritizing confidentiality of results and opportunities for participants to reach out with concerns.

Cultural Factors Affecting Research

• Cultural Sensitivity: Different cultural groups may respond differently to studies—variances in social support mechanisms (e.g., Asian Americans) revealed differences in willingness to disclose personal issues.

Replication in Research

• Exact Replication: Reproduces the methodology of the original study precisely.
• Conceptual Replication: Tests the same hypothesis with different methods to confirm findings.
• Importance of replications underscores the reliability and generalizability of research outcomes.
• Generalizability issues emphasized through replication efforts across diverse populations and settings.

Importance of Research in Practical Life

• Application of psychological research across various fields including health, law, education, and social support.
• Advocates for women in clinical trials and recognition of sex differences in biomedical research as a critical facet to improve outcomes.